The entanglement entropy of a subregion of a field theory in a thermal state has an extensive component which scales with the volume of the subregion, when the subregion is large. In holography, previous work by Liu-Mezei [1]}, [2]} has shown that the HRT surface is consistent with this volume scaling in static situations. See also [3]}, [4]}, [5]}, [6]} for related techniques. In time-dependent situations, it is widely expected that the HRT surface continues to be consistent with the volume-law, although a formal check is lacking. In this paper, we take the first steps toward that direction by generalizing the Liu-Mezei technique to non-static situations. Specifically, we will consider a boundary subregion not lying on a static timeslice, with the bulk geometry taken to be a static black hole.
